A114640 Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.

1, 1, 0, 0, 2, 1, 1, 0, 1, 1, 3, 2, 3, 3, 5, 0, 4, 5, 2, 3, 8, 6, 5, 10, 9, 9, 16, 14, 12, 16, 17, 10, 17, 15, 16, 19, 35, 17, 34, 37, 40, 31, 54, 36, 60, 61, 58, 63, 88, 58, 88, 87, 91, 84, 115, 93, 116, 108, 115, 130, 190, 143, 165, 214, 219, 200, 255, 240

Offset: 0

Author

Vladeta Jovovic, Feb 18 2006

Keywords

• nonn

Comments

The Heinz numbers of these partitions are given by A109297. - Gus Wiseman, Apr 02 2019

Examples

			From _Gus Wiseman_, Apr 02 2019: (Start)
The initial terms count the following integer partitions:
   0: ()
   1: (1)
   4: (22)
   4: (211)
   5: (221)
   6: (3111)
   8: (41111)
   9: (333)
  10: (511111)
  10: (3331)
  10: (322111)
  11: (332111)
  11: (322211)
  12: (6111111)
  12: (4221111)
  12: (33222)
  13: (33322)
  13: (333211)
  13: (332221)
  14: (71111111)
  14: (52211111)
  14: (4421111)
  14: (4222211)
  14: (333221)
(End)
		

Crossrefs

Cf. A052335, A087153, A109297, A114639, A115584, A117144, A276429, A324572, A325132, A336031.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],Union[#]==Union[Length/@Split[#]]&]],{n,0,30}] (* Gus Wiseman, Apr 02 2019 *)

Extensions

More terms from Alois P. Heinz, Aug 09 2016